UInt64
Defined in: lib/provable/int.ts:30
A 64 bit unsigned integer with values ranging from 0 to 18,446,744,073,709,551,615.
Extends
CircuitValue
Constructors
Constructor
new UInt64(x: string | number | bigint | FieldVar | UInt64 | UInt32): UInt64;
Defined in: lib/provable/int.ts:40
Create a UInt64.
The max value of a UInt64 is 2^64 - 1 = UInt64.MAXINT().
Warning: Cannot overflow, an error is thrown if the result is greater than UInt64.MAXINT()
Parameters
x
string | number | bigint | FieldVar | UInt64 | UInt32
Returns
UInt64
Overrides
CircuitValue.constructor
Properties
value
value: Field;
Defined in: lib/provable/int.ts:31
NUM_BITS
static NUM_BITS: number = 64;
Defined in: lib/provable/int.ts:32
Unsafe
static Unsafe: {
fromField: UInt64;
};
Defined in: lib/provable/int.ts:48
fromField()
fromField(x: Field): UInt64;
Create a UInt64 from a Field without constraining its range.
Warning: This is unsafe, because it does not prove that the input Field actually fits in 64 bits.
Only use this if you know what you are doing, otherwise use the safe UInt64.from.
Parameters
x
Returns
UInt64
Accessors
one
Get Signature
get static one(): UInt64;
Defined in: lib/provable/int.ts:69
Static method to create a UInt64 with value 1.
Returns
UInt64
zero
Get Signature
get static zero(): UInt64;
Defined in: lib/provable/int.ts:63
Static method to create a UInt64 with value 0.
Returns
UInt64
Methods
add()
add(y: number | UInt64): UInt64;
Defined in: lib/provable/int.ts:232
Addition with overflow checking.
Parameters
y
number | UInt64
Returns
UInt64
addMod64()
addMod64(y: UInt64): UInt64;
Defined in: lib/provable/int.ts:157
Addition modulo 2^64. Check Gadgets.addMod64 for a detailed description.
Parameters
y
UInt64
Returns
UInt64
and()
and(x: UInt64): UInt64;
Defined in: lib/provable/int.ts:400
Bitwise AND gadget on UInt64 elements. Equivalent to the bitwise AND & operator in JavaScript.
The AND gate works by comparing two bits and returning 1 if both bits are 1, and 0 otherwise.
It can be checked by a double generic gate that verifies the following relationship between the values below.
The generic gate verifies:
a + b = sum and the conjunction equation 2 * and = sum - xor
Where:
a + b = sum
a ^ b = xor
a & b = and
You can find more details about the implementation in the Mina book
Parameters
x
UInt64
Returns
UInt64
Example
let a = UInt64.from(3); // ... 000011
let b = UInt64.from(5); // ... 000101
let c = a.and(b); // ... 000001
c.assertEquals(1);
assertEquals()
assertEquals(x: this): void;
Defined in: lib/provable/types/circuit-value.ts:121
Parameters
x
this
Returns
void
Inherited from
CircuitValue.assertEquals
assertGreaterThan()
assertGreaterThan(y: UInt64, message?: string): void;
Defined in: lib/provable/int.ts:482
Asserts that a UInt64 is greater than another one.
Parameters
y
UInt64
message?
string
Returns
void
assertGreaterThanOrEqual()
assertGreaterThanOrEqual(y: UInt64, message?: string): void;
Defined in: lib/provable/int.ts:496
Asserts that a UInt64 is greater than or equal to another one.
Parameters
y
UInt64
message?
string
Returns
void
assertLessThan()
assertLessThan(y: UInt64, message?: string): void;
Defined in: lib/provable/int.ts:462
Asserts that a UInt64 is less than another one.
Parameters
y
UInt64
message?
string
Returns
void
assertLessThanOrEqual()
assertLessThanOrEqual(y: UInt64, message?: string): void;
Defined in: lib/provable/int.ts:436
Asserts that a UInt64 is less than or equal to another one.
Parameters
y
UInt64
message?
string
Returns
void
div()
div(y: number | UInt64): UInt64;
Defined in: lib/provable/int.ts:206
Integer division.
x.div(y) returns the floor of x / y, that is, the greatest
z such that z * y <= x.
Parameters
y
number | UInt64
Returns
UInt64
divMod()
divMod(y: string | number | UInt64): {
quotient: UInt64;
rest: UInt64;
};
Defined in: lib/provable/int.ts:166
Integer division with remainder.
x.divMod(y) returns the quotient and the remainder.
Parameters
y
string | number | UInt64
Returns
{
quotient: UInt64;
rest: UInt64;
}
quotient
quotient: UInt64;
rest
rest: UInt64;
equals()
equals(x: this): Bool;
Defined in: lib/provable/types/circuit-value.ts:117
Parameters
x
this
Returns
Inherited from
CircuitValue.equals
greaterThan()
greaterThan(y: UInt64): Bool;
Defined in: lib/provable/int.ts:475
Checks if a UInt64 is greater than another one.
Parameters
y
UInt64
Returns
greaterThanOrEqual()
greaterThanOrEqual(y: UInt64): Bool;
Defined in: lib/provable/int.ts:489
Checks if a UInt64 is greater than or equal to another one.
Parameters
y
UInt64
Returns
isConstant()
isConstant(): boolean;
Defined in: lib/provable/types/circuit-value.ts:125
Returns
boolean
Inherited from
CircuitValue.isConstant
leftShift()
leftShift(bits: number): UInt64;
Defined in: lib/provable/int.ts:350
Performs a left shift operation on the provided UInt64 element.
This operation is similar to the << shift operation in JavaScript,
where bits are shifted to the left, and the overflowing bits are discarded.
It’s important to note that these operations are performed considering the big-endian 64-bit representation of the number, where the most significant (64th) bit is on the left end and the least significant bit is on the right end.
Parameters
bits
number
Amount of bits to shift the UInt64 element to the left. The amount should be between 0 and 64 (or else the shift will fail).
Returns
UInt64
Example
const x = UInt64.from(0b001100); // 12 in binary
const y = x.leftShift(2); // left shift by 2 bits
y.assertEquals(0b110000); // 48 in binary
lessThan()
lessThan(y: UInt64): Bool;
Defined in: lib/provable/int.ts:450
Checks if a UInt64 is less than another one.
Parameters
y
UInt64
Returns
lessThanOrEqual()
lessThanOrEqual(y: UInt64): Bool;
Defined in: lib/provable/int.ts:424
Checks if a UInt64 is less than or equal to another one.
Parameters
y
UInt64
Returns
mod()
mod(y: number | UInt64): UInt64;
Defined in: lib/provable/int.ts:216
Integer remainder.
x.mod(y) returns the value z such that 0 <= z < y and
x - z is divisible by y.
Parameters
y
number | UInt64
Returns
UInt64
mul()
mul(y: number | UInt64): UInt64;
Defined in: lib/provable/int.ts:223
Multiplication with overflow checking.
Parameters
y
number | UInt64
Returns
UInt64
not()
not(): UInt64;
Defined in: lib/provable/int.ts:297
Bitwise NOT gate on Field elements. Similar to the [bitwise
NOT ~ operator in JavaScript](https://developer.mozilla.org/en-US/docs/
Web/JavaScript/Reference/Operators/Bitwise_NOT).
Note: The NOT gate operates over 64 bit for UInt64 types.
A NOT gate works by returning 1 in each bit position if the
corresponding bit of the operand is 0, and returning 0 if the
corresponding bit of the operand is 1.
NOT is implemented as a subtraction of the input from the all one bitmask
You can find more details about the implementation in the Mina book
Returns
UInt64
Example
// NOTing 4 bits with the unchecked version
let a = UInt64.from(0b0101);
let b = a.not();
console.log(b.toBigInt().toString(2));
// 1111111111111111111111111111111111111111111111111111111111111010
or()
or(x: UInt64): UInt64;
Defined in: lib/provable/int.ts:417
Bitwise OR gadget on UInt64 elements. Equivalent to the bitwise OR | operator in JavaScript.
The OR gate works by comparing two bits and returning 1 if at least one bit is 1, and 0 otherwise.
Parameters
x
UInt64
Returns
UInt64
Example
let a = UInt64.from(3); // ... 000011
let b = UInt64.from(5); // ... 000101
let c = a.or(b); // ... 000111
c.assertEquals(7);
rightShift()
rightShift(bits: number): UInt64;
Defined in: lib/provable/int.ts:371
Performs a right shift operation on the provided UInt64 element.
This operation is similar to the >> shift operation in JavaScript,
where bits are shifted to the right, and the overflowing bits are discarded.
It’s important to note that these operations are performed considering the big-endian 64-bit representation of the number, where the most significant (64th) bit is on the left end and the least significant bit is on the right end.
Parameters
bits
number
Amount of bits to shift the UInt64 element to the right. The amount should be between 0 and 64 (or else the shift will fail).
Returns
UInt64
Example
const x = UInt64.from(0b001100); // 12 in binary
const y = x.rightShift(2); // right shift by 2 bits
y.assertEquals(0b000011); // 3 in binary
rotate()
rotate(bits: number, direction: "left" | "right"): UInt64;
Defined in: lib/provable/int.ts:329
A (left and right) rotation operates similarly to the shift operation (<< for left and >> for right) in JavaScript,
with the distinction that the bits are circulated to the opposite end of a 64-bit representation rather than being discarded.
For a left rotation, this means that bits shifted off the left end reappear at the right end.
Conversely, for a right rotation, bits shifted off the right end reappear at the left end.
It’s important to note that these operations are performed considering the big-endian 64-bit representation of the number,
where the most significant (64th) bit is on the left end and the least significant bit is on the right end.
The direction parameter is a string that accepts either 'left' or 'right', determining the direction of the rotation.
To safely use rotate(), you need to make sure that the value passed in is range-checked to 64 bits;
for example, using Gadgets.rangeCheck64.
You can find more details about the implementation in the Mina book
Parameters
bits
number
amount of bits to rotate this UInt64 element with.
direction
left or right rotation direction.
"left" | "right"
Returns
UInt64
Example
const x = UInt64.from(0b001100);
const y = x.rotate(2, 'left');
const z = x.rotate(2, 'right'); // right rotation by 2 bits
y.assertEquals(0b110000);
z.assertEquals(0b000011);
sub()
sub(y: number | UInt64): UInt64;
Defined in: lib/provable/int.ts:241
Subtraction with underflow checking.
Parameters
y
number | UInt64
Returns
UInt64
toBigInt()
toBigInt(): bigint;
Defined in: lib/provable/int.ts:83
Turns the UInt64 into a BigInt.
Returns
bigint
toBits()
toBits(length: number): Bool[];
Defined in: lib/provable/int.ts:550
Returns an array of Bool elements representing little endian binary representation of this UInt64 element.
If you use the optional length argument, proves that the UInt64 element fits in length bits.
The length has to be between 0 and 64 and the method throws if it isn't.
Warning: The cost of this operation in a zk proof depends on the length you specify,
which by default is 64 bits. Prefer to pass a smaller length if possible.
Parameters
length
number = 64
the number of bits to fit the element. If the element does not fit in length bits, the functions throws an error.
Returns
Bool[]
An array of Bool element representing little endian binary representation of this UInt64.
toBytes()
toBytes(): [UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8];
Defined in: lib/provable/int.ts:511
Split a UInt64 into 8 UInt8s, in little-endian order.
Returns
[UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8]
toBytesBE()
toBytesBE(): [UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8];
Defined in: lib/provable/int.ts:518
Split a UInt64 into 8 UInt8s, in big-endian order.
Returns
[UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8, UInt8]
toConstant()
toConstant(): this;
Defined in: lib/provable/types/circuit-value.ts:113
Returns
this
Inherited from
CircuitValue.toConstant
toFields()
toFields(): Field[];
Defined in: lib/provable/types/circuit-value.ts:79
Returns
Field[]
Inherited from
CircuitValue.toFields
toJSON()
toJSON(): any;
Defined in: lib/provable/types/circuit-value.ts:109
Returns
any
Inherited from
CircuitValue.toJSON
toString()
toString(): string;
Defined in: lib/provable/int.ts:76
Turns the UInt64 into a string.
Returns
string
toUInt32()
toUInt32(): UInt32;
Defined in: lib/provable/int.ts:90
Turns the UInt64 into a UInt32, asserting that it fits in 32 bits.
Returns
toUInt32Clamped()
toUInt32Clamped(): UInt32;
Defined in: lib/provable/int.ts:102
Turns the UInt64 into a UInt32, clamping to the 32 bits range if it's too large.
UInt64.from(4294967296).toUInt32Clamped().toString(); // "4294967295"
Returns
xor()
xor(x: UInt64): UInt64;
Defined in: lib/provable/int.ts:266
Bitwise XOR gadget on Field elements. Equivalent to the bitwise XOR ^ operator in JavaScript.
A XOR gate works by comparing two bits and returning 1 if two bits differ, and 0 if two bits are equal.
This gadget builds a chain of XOR gates recursively.
You can find more details about the implementation in the Mina book
Parameters
x
UInt64
UInt64 element to XOR.
Returns
UInt64
Example
let a = UInt64.from(0b0101);
let b = UInt64.from(0b0011);
let c = a.xor(b);
c.assertEquals(0b0110);
check()
static check(x: UInt64): void;
Defined in: lib/provable/int.ts:108
Parameters
x
UInt64
Returns
void
Overrides
CircuitValue.check
empty()
static empty<T>(): InstanceType<T>;
Defined in: lib/provable/types/circuit-value.ts:205
Type Parameters
T
T extends AnyConstructor
Returns
InstanceType<T>
Inherited from
CircuitValue.empty
from()
static from(x: string | number | bigint | UInt64 | UInt32): UInt64;
Defined in: lib/provable/int.ts:142
Creates a new UInt64.
Parameters
x
string | number | bigint | UInt64 | UInt32
Returns
UInt64
fromBits()
static fromBits(bits: (boolean | Bool)[]): UInt64;
Defined in: lib/provable/int.ts:574
Convert a bit array into a UInt64 element using little endian binary representation
The method throws if the given bits do not fit in a single UInt64 element. In this case, no more than 64 bits are allowed.
Important: If the given bits array is an array of booleans or Bool elements that all are constant,
the resulting UInt64 element will be a constant as well. Or else, if the given array is a mixture of constants and variables of Bool type,
the resulting UInt64 will be a variable as well.
Parameters
bits
(boolean | Bool)[]
An array of Bool or boolean type.
Returns
UInt64
A UInt64 element matching the little endian binary representation of the given bits array.
fromBytes()
static fromBytes(bytes: UInt8[]): UInt64;
Defined in: lib/provable/int.ts:525
Combine 8 UInt8s into a UInt64, in little-endian order.
Parameters
bytes
UInt8[]
Returns
UInt64
fromBytesBE()
static fromBytesBE(bytes: UInt8[]): UInt64;
Defined in: lib/provable/int.ts:533
Combine 8 UInt8s into a UInt64, in big-endian order.
Parameters
bytes
UInt8[]
Returns
UInt64
fromFields()
static fromFields<T>(this: T, xs: Field[]): InstanceType<T>;
Defined in: lib/provable/types/circuit-value.ts:129
Type Parameters
T
T extends AnyConstructor
Parameters
this
T
xs
Field[]
Returns
InstanceType<T>
Inherited from
CircuitValue.fromFields
fromJSON()
static fromJSON<T>(x: string): InstanceType<T>;
Defined in: lib/provable/int.ts:126
Decodes a JSON-like object into this structure.
Type Parameters
T
T extends AnyConstructor
Parameters
x
string
Returns
InstanceType<T>
Overrides
CircuitValue.fromJSON
fromObject()
static fromObject<T>(this: T, value: NonMethods<InstanceType<T>>): InstanceType<T>;
Defined in: lib/provable/types/circuit-value.ts:30
Type Parameters
T
T extends AnyConstructor
Parameters
this
T
value
NonMethods<InstanceType<T>>
Returns
InstanceType<T>
Inherited from
CircuitValue.fromObject
fromValue()
static fromValue<T>(x: number | bigint | UInt64): InstanceType<T>;
Defined in: lib/provable/int.ts:504
Type Parameters
T
T extends AnyConstructor
Parameters
x
number | bigint | UInt64
Returns
InstanceType<T>
Overrides
CircuitValue.fromValue
MAXINT()
static MAXINT(): UInt64;
Defined in: lib/provable/int.ts:150
Creates a UInt64 with a value of 18,446,744,073,709,551,615.
Returns
UInt64
sizeInFields()
static sizeInFields(): number;
Defined in: lib/provable/types/circuit-value.ts:37
Returns
number
Inherited from
CircuitValue.sizeInFields
toAuxiliary()
static toAuxiliary(): [];
Defined in: lib/provable/types/circuit-value.ts:56
Returns
[]
Inherited from
CircuitValue.toAuxiliary
toCanonical()
static toCanonical<T>(this: T, value: InstanceType<T>): InstanceType<T>;
Defined in: lib/provable/types/circuit-value.ts:161
Type Parameters
T
T extends AnyConstructor
Parameters
this
T
value
InstanceType<T>
Returns
InstanceType<T>
Inherited from
CircuitValue.toCanonical
toConstant()
static toConstant<T>(this: T, t: InstanceType<T>): InstanceType<T>;
Defined in: lib/provable/types/circuit-value.ts:170
Type Parameters
T
T extends AnyConstructor
Parameters
this
T
t
InstanceType<T>
Returns
InstanceType<T>
Inherited from
CircuitValue.toConstant
toFields()
static toFields<T>(this: T, v: InstanceType<T>): Field[];
Defined in: lib/provable/types/circuit-value.ts:42
Type Parameters
T
T extends AnyConstructor
Parameters
this
T
v
InstanceType<T>
Returns
Field[]
Inherited from
CircuitValue.toFields
toInput()
static toInput(x: UInt64): HashInput;
Defined in: lib/provable/int.ts:112
Parameters
x
UInt64
Returns
HashInput
Overrides
CircuitValue.toInput
toJSON()
static toJSON(x: UInt64): string;
Defined in: lib/provable/int.ts:119
Encodes this structure into a JSON-like object.
Parameters
x
UInt64
Returns
string
Overrides
CircuitValue.toJSON
toValue()
static toValue(x: UInt64): bigint;
Defined in: lib/provable/int.ts:500
Parameters
x
UInt64
Returns
bigint
Overrides
CircuitValue.toValue